# Just hanging around - part3

Classical Mechanics Level 5

If the time period of SHM of rectangular block can be represented as $T=2\pi \sqrt{\frac{m(\sqrt a +b)}{ck}}$

Find the value of $$a+b$$. Give your answer to 2 decimal places.

Details and Assumptions:

• Pulley has sufficient friction for Pure Rolling and mass=m & strings are light and inextensible.

• Gravity is present.

• Zig-zag lines in fig represents spring of spring constant $$k$$ and $$2k$$ as shown.

• a is a square-free integer and the fraction is in simplest form.

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